More specifically, I work in the areas of Modal and Description Logics, ontologies and the logical foundations of the Semantic Web, non-monotonic reasoning and abduction, spatial reasoning, combination techniques for logics, models for conceptual blending, and the formalisation of core concepts in cognition such as 'affordances' and 'image schemas'. I am also interested in philosophical logic and in the History and Philosophy of Logic and Mathematics.

My published work is mainly in the following areas (click to expand):

Cognitive Modelling for AI

Cognitive linguistics introduced image schemas as a missing link between embodied experiences and high-level conceptualisation in language and metaphorical thinking. They are described as the abstract spatio-temporal relationships that function as conceptual building blocks for everyday concepts and events.

Although there is increasing interest in the area of cognitively motivated artificial intelligence, where image schemas are suggested to be a core piece in the puzzle to model human-level conceptualisation and reasoning, so far rather few formal logical approaches can be found in the literature, in particular regarding attention to the dynamic aspects of image schemas. A fundamental problem here is that the typical mainstream approaches in contemporary KR do not map well to various scenarios found in image schema modelling.

In a series of papers, we have been exploring the ontological organisation of image schemas, and pursued novel logical formalisations of this key concept. Formalisations of image schemas have strong relevance in particular both for computational theories of conceptual blending (where they can serve as the generic spaces), as well as for cognitive AI and Robotics in general (where they interact deeply with the idea of affordance).

Computational Creativity

Within the project COINVENT I work on computational creativity, in particular conceptual blending, concept invention, and their computational realisation.

COINVENT is a high-profile international research project funded by the European Commission’s 7th Framework Programme. It aims at advancing the formal understanding of creativity by developing a computationally feasible, cognitively-inspired formal model of concept invention, drawing from interdisciplinary research results from cognitive science, artificial intelligence, formal methods and computational creativity, and validating it for mathematical reasoning and melody harmonisation.

My responsibility as PI in the COINVENT project is to help provide a general formalisation of the Unified Concept Theory proposed by the late Joseph Goguen, to develop a logical framework for the highly influential idea of conceptual blending as introduced by Fauconnier and Turner in the 1990s, and to advance the understanding and to study the heuristics of selecting ‘good’ concepts. COINVENT will also use the Distributed Ontology Language DOL (visit OntoIOp.org) and build a collection of (common-sense) ontologies to steer conceptual blending, deploying them in conceptportal.org, a node in the federated Ontohub.org repository.

Standardising the Distributed Ontology Language DOL

The Distributed Ontology Language (DOL) is currently under standardisation within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37/SC 3. It aims at providing a unified framework for (1) ontologies formalised in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies.

Ontologies play an increasingly important role in various areas of Knowledge Representation, ranging from the life sciences and engineering domains to linguistic semantics. In the process, ontologies are being designed in a broad spectrum of logics, with considerably varying expressivity and supporting quite different reasoning methods, necessitating an in-depth understanding of the concepts of modularity and formal structuring as applied to ontologies.

Therefore, together with Till Mossakowski, Dominik Lücke, and Mihai Codescu, we are analysing in detail the application of formal structuring methods as deployed in algebraic formal specification in software engineering to ontologies. In particular, we employ the Heterogeneous Tool Set HETS for bringing these techniques into the world of ontological engineering.

A comprehensive overview elaborating on the notion of 'hyperontology' can be found here.

With Joana Hois, and John Bateman, I studied the problem of combining ontological representations of (spatial) natural language with various spatial calculi. In particular, we investigated problems in this combination relating to underspecifications of context in natural language, issues of similarity and vagueness, employing ideas from counterpart theory, as well as applying ideas from conceptual blending theory to ontologies.

Abduction for Ontologies

With Corinna Elsenbroich and Ulrike Sattler, I worked on abductive reasoning techniques for ontologies. This is a very interesting area from an application point of view as abduction can be used to define new, and highly useful, reasoning tasks over ontologies. Prominent application areas include diagnosis using medical ontologies or problems in spatial navigation. A first paper can be found here.

Extending Expressive Description Logics

Together with Ian Horrocks and Ulrike Sattler, I have been working on extending the expressivity of the description logic SHOIN underlying the web ontology language OWL-DL.

We defined a logic, called SROIQ, that adds numerous expressive means that were suggested to us by ontology developers as useful additions to OWL-DL, making it more useful in practise. SROIQ is carefully designed to remain decidable and, in particular, to be efficiently implementable building on the succesful implementations of reasoners such as FaCT++.

The logic SROIQ has been adopted as the logical basis for the first successor to OWL, OWL 2 .

Combining Logics: E-connections

The theory of E-connections, developed jointly with Carsten Lutz, Frank Wolter, and Michael Zakharyaschev, is a methodology for combining knowledge representation and reasoning formalisms that is rather expressive, natural from a semantical point of view, and which is very well-behaved computationally in the sense that the combination of decidable formalisms is again decidable, and which, nonetheless, allows non-trivial interactions between the combined components.

In E-connections, a finite number of formalisms are `connected' by relations relating entities across different domains, intended to capture different aspects or representations of the `same object'. For instance, an `abstract' object of a description logic can be related via a relation R to its life-span in a temporal logic as well as to its spatial extension in a spatial logic.

E-connections have found wide recognition in various areas of applied logic. Moreover, it has been realised that besides their original purpose as a powerful framework for integrating logical formalisms of diverse characteristics, they also have great potential as a formalism employed in the Semantic Web, in particular concerning the problem of modularity for web ontologies.

Spatial Logics of Distance

Working with Holger Sturm, Nobu-Yuki Suzuki, Frank Wolter, and Michael Zakharyaschev, I studied Logics of Distance. These are modal (hybrid) logics whose modal operators introduce a quantitative notion of distance or similarity, thus widening the scope of the typically `qualitative' spatial representation and reasoning.

Such a distance operator would say, for instance, that everywhere at distance less or equal r (a rational number), formula φ holds. We found decidable distance logics, investigated their complexity, axiomatisations, and logical properties like interpolation.

Besides applications in spatial reasoning, these logics can also be interpreted as dealing with similarity measures (inducing a distance function) which are ubiquitous in Knowledge Representation. For instance, similarity measures appear naturally in an analysis of definitions of concepts by prototypes, or in the classification of proteins in Bioinformatics.

Semantics of Modal Predicate Logics

Together with Marcus Kracht, I have been investigating various semantics for languages of modal predicate logics that combine modalities (such as `possibility' and `necessity') with first-order quantification over individuals.

These languages are notorious for the semantic difficulties they pose, and their investigation has a long and tangled history. We are particularly interested in finding general but still `natural' semantics, and in an analysis of the different notions of world, accessibility, and object. Interesting applications include, for instance, an analysis of notions of persistence through time, or ontologies of space-time theories, and the progress made in the area (in particular concerning decidable fragments) has revived an interest in these languages also as knowledge representation formalisms. Specifically, the development of so-called `generalised counterpart-theoretic semantics' in this context directly influenced the development of E-connections.